The sensitive plant (Mimosa pudica) is a remarkable little plant whose characteristic feature is its ability to droop its leaves when disturbed:

Apparently, this ability to droop rests on the cells in the leaves of the sensitive plant being able to draw water out of themselves through changes in intracellular ion concentrations, which makes the leaves less turgid.

What I'm hazy about is how the plant "senses" vibrations. Plants don't really have a nervous system to speak of; how then does the sensitive plant "know" to droop when disturbed?

The leaves are not actually drooping, they are pivoting upwards. Drooping would be easier, but would not perform the crucial function of the closure, which is to reduce evapotranspiration from the stomata which are mostly on the upper (adaxial) leaf surface.
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Richard Smith-UnnaFeb 2 '12 at 17:29

3 Answers
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In fact, the idea of a plant nervous system is quite serious and constantly developing; of course those are rather local, simple signal pathways rather than an "animalian" centralized global network, but they use similar mechanisms -- depolarisation waves, neurotransmitter-like compounds, specialized cells... Here is a review paper by Brenner et al.

In the case of Mimosa, there is a good paper summing up Takao Sibaoka's long research of the topic.

In short, it seems that its petioles' phloem has cells which have polarized membranes and can trigger depolarization due to a mechanical stimulation. The signal then propagates to the corresponding pulvinus by a mixture of electrical and Cl- depolarization waves.

In the pulvinus, this signal triggers a second depolarization which coordinates the pulvinus' cells to trigger water pumping responsible for the leaf drop.

The transmission to the adjacent leaves is most likely mechanical, i.e. the movement of one dropping leaf excites another.

Haswell, Peyronnet, et al (2008) have shown that plants have some of the same mechanosensitive ion channels that E. coli does. The work was on the roots of Arabidopsis and not the plant you are investigating, but the mechanism could be similar.

It would not seem that vibration plays a role, as it the plant seems responsive to the touch of the human rather than his/her approach to the leaf. This could rule out air currents as a mechanism (but J.M. has noted in the comments that they do fold up when you blow on them).

Some additional notes- I have grown TickleMe Plants (sensitive plants) for years and I have seen the plants close their leaves as a reaction to the vibrations caused by my foot steps as well as blowing on the plant and placing the plant in cold, very hot and dark environments. In addition I have found the plant's ablity to detect vibrations I have observed to be dependent on temperature and the time of day. Some of this information can be found in The TickleMe Plant Book found at http://www.ticklemeplant.com I am unable to specifically say what the mechanism is that detects the vibrations and causes the TickleMe Plants turgor pressure to change. I look forward to more answers.